Solve for $x$ and $y$ by deriving an expression for $x$ from the second equation, and substituting it back into the first equation. $\begin{align*}-3x-5y &= -2 \\ x-9y &= -6\end{align*}$
Explanation: Begin by moving the $y$ -term in the second equation to the right side of the equation. $x = {9y-6}$ Substitute this expression for $x$ in the first equation. $-3({9y - 6}) - 5y = -2$ $-27y + 18 - 5y = -2$ Simplify by combining terms, then solve for $y$ $-32y + 18 = -2$ $-32y = -20$ $y = \dfrac{5}{8}$ Substitute $\dfrac{5}{8}$ for $y$ in the top equation. $-3x-5( \dfrac{5}{8}) = -2$ $-3x-\dfrac{25}{8} = -2$ $-3x = \dfrac{9}{8}$ $x = -\dfrac{3}{8}$ The solution is $\enspace x = -\dfrac{3}{8}, \enspace y = \dfrac{5}{8}$.